Minimum coloring random and semi-random graphs in polynomial expected time

We present new algorithms for k-coloring and minimum (χ(G)-) coloring random and semi-random k-colorable graphs in polynomial expected time. The random graphs are drawn from the G(n,p,k) model and the semi-random graphs are drawn from the G_SB(n,p,k) model. In both models, an adversary initially splits the n vertices into k color classes, each of size Θ(n). Then the edges between vertices in different color classes are chosen one by one, according to some probability distribution. The model G_SB(n,p,k) was introduced by A. Blum (1991) and with respect to randomness, it lies between the random model G(n,p,k) where all edges are chosen with equal probability and the worst-case model